The plan recently made $285 million in private markets commitments.
The retirement system will interview the finalists at its December finance committee meeting.
The board hired an intermediate manager to replace a short-term bond mandate.
The retirement system also approved a search for a multi-asset credit manager at the end of August.
The commitments include two new manager relationships for the council.
The plan is looking to invest up to $35 million across the two strategies.
The plan will look to conclude its private markets consultant search next month.
The pension plan will conduct a search for one or more core/core-plus real estate managers as part of a newly approved real assets fiscal year 2026 investment plan.
The retirement system established a new 5% target to the asset class last year.
The new asset allocation includes a 5% private credit target.